I bought a small cake, plus a lighter and a number one and number six shaped candle.
The original words are number-one shaped candle and number-six shaped candle. Is it correct to drop the hyphen when used as in the sentence above?
This comes down to a matter of style and personal preference.
For example, the Chicago Manual of Style has specific rules regarding when to hyphenate and when not to, for a number of different situations concerning the use of numbers, here's an example (there are more in the linked chapter):
numbers, spelled out
Twenty-one through ninety-nine hyphenated; others open. See also fractions, simple..
But unless you are writing a formal paper (in which case I would check to see if there is any style guide in use which might specify a rule) you can use hyphenated or open according to your personal sense of style. The key is that you should be consistent with whichever option you choose and don't mix open with hyphenated for the same number in the same document.